Penultimate Unit: 108° angle for pentagonal faces

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The instructions presented here are for the simplest version of the unit, which results in 108° angles and thus can build faces that are regular pentagons. The construction is approximate, but it is good enough for any practical uses. The simplest example of using such units is shown below — building a regular dodecahedron. It has 30 edges and thus requires 30 units. Here are some examples of what else you can build by combining 108° units with other variants (including units with different angles at each end):

See other sections of this tutorial for instructions on folding and connecting other variants of this unit.

Step 1
1. Start with a square
Step 2
2. Valley fold
Step 3
3. Valley fold
Step 4
4. Fold as in previous step on the back
Step 5
5. Fold down corner
Step 6
6. Fold the other corner
Step 7
7. Valley fold the diagonal of the 2:1 rectangle in central part of the module (only one of the two diagonals works!)
Step 8
8. Module seen from the other side
Step 9
9. For making a dodecahedron, you will need 30 units
Step 10
10. This and a few following steps show how to connect three units that form a single vertex
Step 11
11. Put the tab at the end of a unit inside the pocket formed between layers on the side of another unit
Step 12
Step 13
Step 14
14. A single vertex is complete
Step 15
15. Same vertex seen from the other side. Now keep adding more units as shown in following images. All vertices have the same structure as this first one.
Step 16
Step 17
Step 18
Step 19
19. The last vertex may be harder to close than those before, but its structure is the same. Each unit holds its neighbor’s tab and has its own tab inserted into the other neighbor.
Step 20
Step 21
Step 22
Step 23
23. Last vertex fully closed
Step 24
24. Complete dodecahedron